Increasing population and consumption are placing unprecedented demands on agriculture and natural resources. Today, approximately a billion people are chronically malnourished while our agricultural systems are concurrently degrading land, water, biodiversity and climate on a global scale. To meet the world's future food security and sustainability needs, food production must grow substantially while, at the same time, agriculture's environmental footprint must shrink dramatically. Here we analyse solutions to this dilemma, showing that tremendous progress could be made by halting agricultural expansion, closing 'yield gaps' on underperforming lands, increasing cropping efficiency, shifting diets and reducing waste. Together, these strategies could double food production while greatly reducing the environmental impacts of agriculture.

https://escholarship.org/content/qt6xw5g085/qt6xw5g085.pdf?t=ovfwpc

Solutions for a cultivated planet

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Nonlinear Programming: A Unified Approach

An acreage supply response model is developed under expected utility maximization. The resulting framework is used to specify and estimate a system of risk-responsive acreage equations for corn and soybeans in the United States. Particular attention is given to the truncation effects of government price supports on the distribution of corn and soybean prices. Also, a wealth variable is included in the acreage equations. The empirical results indicate that risk and wealth variables play an important role in cornsoybean acreage decisions. The analysis also shows that cross-commodity risk reduction is important in acreage allocation decisions.

Acreage Decisions Under Risk: The Case of Corn and Soybeans

Uncertainty and risk are quintessential features of agricultural production. After a brief overview of the main sources of agricultural risk, we provide an exposition of expected utility theory and of the notion of risk aversion. This is followed by a basic analysis of agricultural production decisions under risk, including some comparative statics results from stylized models. Selected empirical topics are surveyed, with emphasis on risk analyses as they pertain to production decisions at the farm level. Risk management is then discussed, and a synthesis of hedging models is presented. We conclude with a detailed review of agricultural insurance, with emphasis on the moral hazard and adverse selection problems that arise in the context of crop insurance.

Chapter 2 Uncertainty, risk aversion, and risk management for agricultural producers

Production economics problems are often ill-posed. This means that the number of parameters to be estimated is greater than the number of observations. In this article we show how to recover flexible cost functions from very limited data sets using a maximum entropy approach. We also argue that there exists a continuum of analysis between mathematical programming and traditional econometric techniques which is based solely upon the available information. The limiting case of a multi-output cost function recovered using only a single observation of a farmer's allocation decisions can be easily extended to handle more than one observation.

https://papers.ssrn.com/sol3/Delivery.cfm/AJAE_AJAE3180275.pdf?abstractid=3567262&mirid=1

An Analysis of Ill-Posed Production Problems Using Maximum Entropy

Using a celebrated sample of corn response to nitrogen and phosphorus collected by Heady and Pesek, it is shown that a von Liebig model with Mitscherlich regimes is the best interpreter of the experimental data. This assertion is based upon the results of nonnested hypothesis tests among five alternatives. An extension of the test to switching regression models reinforces the superiority of the von Liebig hypothesis for this sample. Cost functions, dual to von Liebig production functions, have continuous derivatives with respect to the parameters and may be easier to estimate when input prices are available.

The von Liebig Hypothesis

Crop responses to fertilizers traditionally have been specified as polynomial functions. Recently, criticisms were raised against such specifications because they force substitution between nutrients and overestimate the optimal fertilizer quantity. With those criticisms, an alternative crop response function was presented in the form of a minimum function which equates the realized output to the production potential associated with a limiting input. In this paper a nonnested test is performed to discriminate between the two rival specifications. The results of this test reject the hypothesis that a crop response is of the polynomial type, while they do not reject the hypothesis that it is of the minimum and plateau type.

Testing a von Liebig Crop Response Function against Polynomial Specifications

A novel control model for technical and economic analysis of fertilizer recommendations is based on Liebig's Law of the Minimum, Mitscherlich's relative yield theory, and the notions of yield plateau and soil fertility carry-over. The empirical model consists of a multistage separable programming specification which maximizes the discounted stream of net revenues subject to crop response and fertility carry-over functions. The model is applied to the wheat-soybean cropping system in Southern Brazil. It is found that, while the optimal fertility target levels are within a small range of those determined by Brazilian agronomists, their maintenance recommendations could be substantially improved. control, relative yield, yield plateau. The analysis of yield response to fertilizers has been recently enriched by an original proposal of Cate and Nelson. These soil scientists suggested that for agronomic purposes and for certain crops, it may be convenient to postulate that the relationship between yield and major nutrients is a linear response and plateau (LRP) function. They argued that this simplified specification is nonetheless capable of capturing the essential information of yield

/pdf/a-new-analytical-framework-for-the-fertilization-problem-ntgzdyqvw6.pdf

A New Analytical Framework for the Fertilization Problem

Two distinct but related approaches for the estimation of von Liebig response functions are presented. The first approach is based upon a two-phase, ordinary least squares procedure combined with bootstrapping for computing the standard errors of the estimates. The second approach generates maximum likelihood estimates of the parameters and can be implemented according to two different parameterizations of the model. Application of the procedures to a sample of experimental data suggests a satisfactory degree of conformity of the results. A test of normality of the disturbance term based upon the estimated residuals failed to reject the null hypothesis, further supporting the maximum likelihood approach. This paper presents two distinct but related approaches for the estimation of von Liebig's response functions. First, a two-phase, ordinary least squares procedure is outlined. Second, maximum likelihood estimates of the parameters are obtained by means of two different reparametrizations of the model. A nonlinear programming computer code is required to implement this approach. An application of the procedures to a sample of experimental data indicates a close conformity among the results. Advantages and limitations of each procedure are discussed in a concluding section.

Quirino Paris

Papers

An Analysis of Ill-Posed Production Problems Using Maximum Entropy

The von Liebig Hypothesis

Testing a von Liebig Crop Response Function against Polynomial Specifications

A New Analytical Framework for the Fertilization Problem

Estimation of von Liebig Response Functions